EularProject 32: 数字1-9排列构成乘法等式

Pandigital products

Problem 32

We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.

The product 7254 is unusual, as the identity, 39 × 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.

Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.

HINT: Some products can be obtained in more than one way so be sure to only include it once in your sum.

Answer:

45228

Completed on Sat, 25 Jul 2015, 15:13

python code:

from math import sqrt
def func(x):
    s0=set(str(x))
    for i in range(2,min(100,int(sqrt(x)+1))):
        if x%i==0:
            s1=set(str(i))
            s2=set(str(x//i))
            s=s0|s1|s2
            if len(s)==9 and ‘0‘ not in s:
                return True
    return False

result=0
for i in range(1000,9999):
    Pstr=str(i)
    if len(set(Pstr))==4 and ‘0‘ not in Pstr:
        if func(i):
            result+=i
            print(i)

print(result)

这里因为要求乘积不能重复，可以考虑对乘积候选项循环判断，把满足条件的加起来，并且很容易反证证明乘积项数字位数只能为4。

数字1-9是一个有趣的问题，更多问题可以参考

http://www.worldofnumbers.com/ninedig1.htm

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